A355703 a(n) = binomial(n, floor(log(n))).

1, 1, 3, 4, 5, 6, 7, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180, 16215, 17296, 18424, 19600, 20825

Offset: 1

Author

Christoph B. Kassir, Jul 14 2022

Keywords

• nonn

Links

• Mathematics Stack Exchange, How to compute asymptotic growth of binomial(n, log(n)).

Crossrefs

Cf. A000195, A007318.

Cf. A001405, A051033, A051036, A051052, A051053.

Programs

Maple

a:= n-> binomial(n, ilog(n)):
seq(a(n), n=1..60);  # Alois P. Heinz, Jul 31 2022

Mathematica

a[n_] := Binomial[n, Floor[Log[n]]]; Array[a, 50] (* Amiram Eldar, Jul 31 2022 *)

PARI

a(n) = binomial(n, floor(log(n))); \\ Michel Marcus, Jul 31 2022

Python

from numpy import log
from math import comb, floor
for n in range(1, 50):
    x = comb(n, floor(log(n)))
    print("{}, ".format(x), end='')